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Math Help - About characteristic of rings

  1. #1
    Junior Member hercules's Avatar
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    About characteristic of rings

    What can be said about the characteristic of a ring R in which x=-x for each x in R?

    Thank You
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    Junior Member hercules's Avatar
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    i picked up some alien signals

    Quote Originally Posted by hercules View Post
    What can be said about the characteristic of a ring R in which x=-x for each x in R?
    Thank You
    I think i got it now. But if anyone has any ideas and suggestions...please do post them ....they will help me understand better.
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    Quote Originally Posted by hercules View Post
    What can be said about the characteristic of a ring R in which x=-x for each x in R?

    Thank You
    The charachteristic is 2. Because if x=-x\implies x + x = 0 in particular 2\cdot 1 = 0.
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    Junior Member hercules's Avatar
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    Quote Originally Posted by ThePerfectHacker View Post
    The charachteristic is 2. Because if x=-x\implies x + x = 0 in particular 2\cdot 1 = 0.
    Why did you pick 1 for x value specifically? (where 2x=0)
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    Quote Originally Posted by hercules View Post
    Why did you pick 1 for x value specifically? (where 2x=0)
    It really works for any value of x. But field charachteristics are defined for 1. Because if 1 + 1 = 0 then it is true for any element. That is why we resrict out attention to 1.
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by hercules View Post
    Why did you pick 1 for x value specifically? (where 2x=0)
    TPH is right. To supplement his comments, read the paragraph right under the definition of the characteristic in your text
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    Junior Member hercules's Avatar
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    Quote Originally Posted by Jhevon View Post
    TPH is right. To supplement his comments, read the paragraph right under the definition of the characteristic in your text

    Isn't that only if ring has unity?

    Don't worry about it ...it just takes me longer to get it but i'll get it.
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  8. #8
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by hercules View Post
    Isn't that only if ring has unity?

    Don't worry about it ...it just takes me longer to get it but i'll get it.
    1 is the unity element. otherwise, we have 2x = 0 for all x in R, so either definition is satisfied. I was just trying to show you why considering 1 was relevant
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    Quote Originally Posted by hercules View Post
    Isn't that only if ring has unity?
    I believe field characheristics are only defined for commutative unitary rings.
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